Work

Integral filling volume, complexity, and integral simplicial volume of $3$-dimensional mapping tori

Year: 2024

Type: article

Abstract: We show that the integral filling volume of a Dehn twist f on a closed oriented surface vanishes, i.e., that the integral simplicial volume of the mapping torus with monodromy f^{n} grows sublinearly with respect to n . We deduce a complete characterization of mapping classes on surfaces with vanishing integral filling volume and, building on results by Purcell and Lackenby on the complexity of mapping tori, we show that, in dimension three, complexity and integral simplicial volume are not Lipschitz equivalent.

Source: Groups Geometry and Dynamics

DOI: 10.4171/ggd/839

Authors: Federica Bertolotti, Roberto Frigerio

Institutions: Scuola Normale Superiore, University of Pisa

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni

Awards: G375838716, G4022907568